# trigonometry equation

• Apr 11th 2007, 04:14 AM
seb
trigonometry equation

if 0 is smaller then or equal to a which is < then 2pi then the equation sina=cos a has how many solutions? what are they? justify.
• Apr 11th 2007, 05:17 AM
CaptainBlack
Quote:

Originally Posted by seb

if 0 is smaller then or equal to a which is < then 2pi then the equation sina=cos a has how many solutions? what are they? justify.

Sketch the curves y=sin(x) and y=cos(x) over the interval (0, 2 pi).

You will observe that there are two points at which the cross, and the
x's for these points are the values for which sin(x)=cos(x) and so are
the values of a that you require.

sin(a)=cos(a)

can be rearranged to tan(a)=1, so one solution is 45 degrees (pi/4 radian)

The other solution is in the third quadrant (where tan is positive) and so

RonL
• Apr 11th 2007, 06:15 AM
Soroban
Hello, seb!

Quote:

if 0 < θ < 2π, then the equation sinθ = cosθ has how many solutions?
What are they? .Justify.

Divide both sides by cosθ, and we have: .tanθ .= .1

The only angles on the inteval [0, 2π) with a tangent of 1 are: .π/4 and 5π/4

Therefore, there are two solutions: .θ .= .π/4, 5π/4